I just watched Batman Under the Red Hood. I loved it, however it talked about the other robins, and (I don't want to give anything away) but it made references to other events in the Batman universe. Where these in other movies or just taken for granted that the audience knows what happened in the past?
The character of Nightwing in the comics, and the film, was once the ORIGINAL robin, Dick Grayson. The robin that dies at the beginning of the film is the 2nd robin, Jason Todd. The comics, and the film, show that the Joker killed him. This film stands alone in relation to all the other Batman films. The animated films are generally one-shot stories without overarching story lines connecting the individual films. Hope this helps